# Design of Experiments

## An Introduction Based on Linear Models

#### By **Max Morris**

Chapman and Hall/CRC – 2010 – 370 pages

Chapman and Hall/CRC – 2010 – 370 pages

Offering deep insight into the connections between design choice and the resulting statistical analysis, **Design of Experiments: An Introduction Based on Linear Models** explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experimental design as a whole within the structure provided by general linear models, rather than as a collection of seemingly unrelated solutions to unique problems.

The core material can be found in the first thirteen chapters. These chapters cover a review of linear statistical models, completely randomized designs, randomized complete blocks designs, Latin squares, analysis of data from orthogonally blocked designs, balanced incomplete block designs, random block effects, split-plot designs, and two-level factorial experiments. The remainder of the text discusses factorial group screening experiments, regression model design, and an introduction to optimal design. To emphasize the practical value of design, most chapters contain a short example of a real-world experiment. Details of the calculations performed using R, along with an overview of the R commands, are provided in an appendix.

This text enables students to fully appreciate the fundamental concepts and techniques of experimental design as well as the real-world value of design. It gives them a profound understanding of how design selection affects the information obtained in an experiment.

the author has succeeded in striking a balance between the choice of topics and depth in discussion for teaching a course. The book is written with a refreshing style and succeeds in conveying the concepts to a reader. The treatment of the subject matter is thorough and the theory is clearly illustrated along with worked examples. Other books are available on similar topics but this book has the advantage that the chapters start with the classical non-matrix-theory approach to introduce the linear model and then converts it into a matrix theory-based linear model. This helps a reader, particularly a beginner, in clearly understanding the transition from a non-matrix approach to a matrix approach and to apply the results of matrix theory over linear models further.

—Shalabh, *Journal of the Royal Statistical Society*, Series A, 2012

Overall, this is a book that is easy to like, with good definitions of designs, few typographical errors, and consistent, straightforward explications of the models … I can picture a lot of students using a text aimed at a broad market design course but who need to understand more about what is going on behind the curtain. Morris’ text also fills that gap very well.

—Gary W. Oehlert, *Biometrics*, May 2012

It is truly my pleasure to read this book … after reading this book, I benefitted by gaining insights into the modeling aspect of experimental design, and consequentially it helps me appreciate the idea of statistical efficiency behind each design and understand the tools used in data analysis. … an excellent reference book that I would recommend to anyone who is serious about learning the nuts and bolts of experimental design and data analysis techniques.

—Rong Pan, *Journal of Quality Technology*, Vol. 43, No. 3, July 2011

**Introduction**

Example: rainfall and grassland

Basic elements of an experiment

Experiments and experiment-like studies

Models and data analysis

**Linear Statistical Models**

Linear vector spaces

Basic linear model

The hat matrix, least-squares estimates, and design information matrix

The partitioned linear model

The reduced normal equations

Linear and quadratic forms

Estimation and information

Hypothesis testing and information

Blocking and information

**Completely Randomized Designs**

Introduction

Models

Matrix formulation

Influence of design on estimation

Influence of design on hypothesis testing

**Randomized Complete Blocks and Related Designs**

Introduction

A model

Matrix formulation

Influence of design on estimation

Influence of design on hypothesis testing

Orthogonality and "Condition E"

**Latin Squares and Related Designs**

Introduction

Replicated Latin squares

A model

Matrix formulation

Influence of design on quality of inference

More general constructions: Graeco-Latin squares

**Some Data Analysis for CRDs and Orthogonally Blocked Designs**

Introduction

Diagnostics

Power transformations

Basic inference

Multiple comparisons

**Balanced Incomplete Block Designs**

Introduction

A model

Matrix formulation

Influence of design on quality of inference

More general constructions

**Random Block Effects**

Introduction

Inter- and intra-block analysis

CBDs and augmented CBDs

BIBDs

Combined estimator

Why can information be "recovered"?

CBD reprise

**Factorial Treatment Structure**

Introduction

An overparameterized model

An equivalent full-rank model

Estimation

Partitioning of variability and hypothesis testing

Factorial experiments as CRDs, CBDs, LSDs, and BIBDs

Model reduction

**Split-Plot Designs**

Introduction

SPD(R,B)

SPD(B,B)

More than two experimental factors

More than two strata of experimental units

**Two-Level Factorial Experiments: Basics**

Introduction

Example: bacteria and nuclease

Two-level factorial structure

Estimation of treatment contrasts

Testing factorial effects

Additional guidelines for model editing

**Two-Level Factorial Experiments: Blocking**

Introduction

Complete blocks

Balanced incomplete block designs

Regular blocks of size 2^{f−1 }

Regular blocks of size 2^{f−2 }

Regular blocks: general case

**Two-Level Factorial Experiments: Fractional Factorials**

Introduction

Regular fractional factorial designs

Analysis

Example: bacteria and bacteriocin

Comparison of fractions

Blocking regular fractional factorial designs

Augmenting regular fractional factorial designs

Irregular fractional factorial designs

**Factorial Group Screening Experiments **

Introduction

Example: semiconductors and simulation

Factorial structure of group screening designs

Group screening design considerations

Case study

**Regression Experiments: First-Order Polynomial Models **

Introduction

Polynomial models

Designs for first-order models

Blocking experiments for first-order models

Split-plot regression experiments

Diagnostics

**Regression Experiments: Second-Order Polynomial Models**

Introduction

Quadratic polynomial models

Designs for second-order models

Design scaling and information

Orthogonal blocking

Split-plot designs

Bias due to omitted model terms

**Introduction to Optimal Design **

Introduction

Optimal design fundamentals

Optimality criteria

Algorithms

**Appendices**

**References**

**Index**

*A Conclusion and Exercises appear at the end of each chapter.*

**Max D. Morris** is a professor in the Department of Statistics and the Department of Industrial and Manufacturing Systems Engineering at Iowa State University. A fellow of the American Statistical Association, Dr. Morris is a recipient of the National Institute of Statistical Sciences Sacks Award for Cross-Disciplinary Research and the American Society for Quality Wilcoxon Prize.

Name: Design of Experiments: An Introduction Based on Linear Models (Hardback) – Chapman and Hall/CRC

Description: By Max Morris. Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models...

Categories: Statistical Theory & Methods, Mathematics & Statistics for Engineers, Statistics for the Biological Sciences